Multilevel Methods for the Poisson-Boltzmann Equation

We consider the numerical solution of the Poisson-Boltzmann equation (PBE), a three-dimensional second order nonlinear elliptic partial differential equation arising in biophysics. This problem has several interesting features impacting numerical algorithms, including discontinuous coefficients representing material interfaces, rapid nonlinearities, and three spatial dimensions. Similar equations occur in various applications, including nuclear physics, semiconductor physics, population genetics, astrophysics, and combustion. In this thesis, we study the PBE, discretizations, and develop multilevel-based methods for approximating the solutions of these types of equations.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Holst, Michael Jay

Contributors dc:contributor

• Saied, Faisal

• Mathematics
• Physics, Molecular
• Computer Science

Identifier

(UMI)AAI9411653

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/72092